Removing internal geometry
Assuming that you are using a release of Blender that is at least 2.77 or newer, then you can use the edit mode boolean tools and save a couple steps.


First select one element of the object in edit mode by linked geometry by
selecting a face, edge, or vertex, and then press L with
your mouse hovering over it.
Press Spacebar and type Boolean and select Mesh: Intersect (Boolean) from the menu, or press Enter when the
option appears in the menu.
Next, press F6 to bring up the options for the tool (or
go to the operator panel in the toolshelf) and change the mode to union.